In Figure (REF ) we present the solutions for \( h(r) \)  with different values of horizons in the left, middle, and right panels that depicting the full continued-fraction solution (REF ) along with its comparison to the near-horizon solution with blue dashed lines and large-\(r\) 
series expansions solution with black dashed lines. We see that
the continued-fraction expansion converges to both of these two approximations. Similar to quadratic gravity, we find two groups of solutions [1]}, [2]}, [3]}. For the first group, the metric function is increasing functions in \( r\ge r_{+} \) . These solutions are generalizations of the Schwarzschild black hole solution and reduce to the Schwarzschild as \(\alpha \rightarrow 0\) .
The non-Schwarzschild solutions are physically distinct from the first group, and as \(\alpha \rightarrow 0\) , it does not go back to the Schwarzschild metric.
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